\documentclass{article} \pagestyle{plain} \newcommand{\F}{{\cal F}} \newcommand{\p}{{\cal P}} \newcommand{\Kprod}{\otimes} \newcommand{\Diag}{\rm Diag\,} \newcommand{\tran}{^T} \newcommand{\diag}{\rm diag\,} \newcommand{\tr}{\rm trace\,} \newcommand{\trace}{\rm trace\,} \newcommand{\beq}{\begin{equation}} \newcommand{\Sn}{{\cal S}^n} \newcommand{\svec}{{\rm svec\,}} \newcommand{\sMat}{{\rm sMat\,}} \newcommand{\hMat}{{\rm hMat\,}} \newcommand{\dsvec}{{\rm dsvec\,}} \newcommand{\sdiag}{{\rm sdiag\,}} \newcommand{\vsMat}{{\rm vsMat\,}} \newcommand{\kvec}{{\rm vec\,}} \newcommand{\kmat}{{\rm Mat\,}} \newcommand{\eeq}{\end{equation}} \newcommand{\nc}{\newcommand} \nc{\Hcal}{{\cal H}} \newcommand{\rank}{{\rm rank\,}} \newcommand{\trian}{{\rm trian\,}} \newcommand{\Trian}{{\rm Trian\,}} \newcommand{\BoDiag}{{\rm B^0Diag\,}} \newcommand{\OoDiag}{{\rm O^0Diag\,}} \newcommand{\arrow}{{\rm arrow\,}} \newcommand{\Arrow}{{\rm Arrow\,}} \newcommand{\bodiag}{{\rm b^0diag\,}} \newcommand{\oodiag}{{\rm o^0diag\,}} \newcommand{\ck}{{\cal C}_k} \newcommand{\dk}{{\cal D}_k} \newcommand{\uu}{{\cal U}} \newcommand{\uk}{{\cal U}_k} \newcommand{\vk}{{\cal V}_k} \newcommand{\wk}{{\cal W}_k} \newcommand{\wm}{{\cal W}_m} \newcommand{\w}{{\cal W}} \newcommand{\wks}{{\cal W}^s_k} \newcommand{\wms}{{\cal W}^s_m} \newcommand{\zk}{{\cal Z}_k} \newcommand{\zks}{{\cal Z}^s_k} \newcommand{\z}{{\cal Z}} \newcommand{\n}{{\cal N}} \newcommand{\ra}{{\cal R}} \newcommand{\q}{{\cal Q}} \newcommand{\s}{{\cal S}_n} \newcommand{\m}{{\cal M}_{n}} \newcommand{\req}[1]{(\ref{#1})} \newcommand{\adj}{{\rm adj\,}} \newcommand{\relint}{{\rm relint\,}} \def\QED{~\rule[-1pt] {8pt}{8pt}\par\medskip ~~} \begin{document} %======================= %======================= \begin{center} \begin{tabular}{|l|rrrrr|rrr|} \hline & Sol. & GLB & ELI & RRD & EVB3 &$\mu_{R1}$ &$\mu_{R2}$&$\mu_{R3}$\\ \hline Rou12 &235528&202272&200024&224278&201337& 208685&220991&227986\\ Rou15 &354210&298548&296705&324869&297958& 306833&323141&324900\\ Rou20 &725522&599948&597045&643346& n.a. & 615549&642448&631680\\ \hline Scr12 & 31410& 27858& 4727& 29872& n.a. & 11117&24230 & 27183\\ Scr15 & 51140& 44737& 10355& 49264& n.a. & 17046&42094 & 40821\\ Scr20 &110030& 86766& 16113& 95113& n.a. & 28535&83026 & 59780\\ \hline Tai12a & 224416 & 195918 & 193124 & n.a. &195673 &203595&215377&220938\\ Tai15a & 388214 & 327501 & 325019 & n.a. &327289 &333437&349476&347908\\ Tai17a & 491812 & 412722 & 408910 & n.a. &410076 &419619&441238&435675\\ Tai20a & 703482 & 580674 & 575831 & n.a. & n.a. &591994&618720&606228\\ Tai25a &1167256 & 962417 & 956657 & n.a. & n.a. &974004 & --~ & --~ \\ Tai30a &1818146 &1504688 &1500407 & n.a. & n.a. &1529135& --~ & --~ \\ \hline Tho30 & 149936 & 90578 & 119254 & 100784 & n.a. &125972& --~ & --~ \\ \hline \end{tabular} ~~\\ {QAPLIB instances 2} \end{center} \begin{center} \begin{tabular}{|l|rrrrr|rrr|} \hline & Sol. & GLB & ELI & RRD & EVB3 &$\mu_{R1}$ &$\mu_{R2}$&$\mu_{R3}$\\ \hline Car10ga& 4954 & 3586 & 4079 & n.a. & 4541 & 4435 & 4853 &4919 \\ Car10gb& 8082 & 6139 & 7211 & n.a. & 7617 & 7600 & 7960 &8035 \\ Car10gc& 8649 & 7030 & 7837 & n.a. & 8233 & 8208 & 8561 &8612 \\ Car10gd& 8843 & 6840 & 8006 & n.a. & 8364 & 8319 & 8666 &8780 \\ Car10ge& 9571 & 7627 & 8672 & n.a. & 8987 & 8910 & 9349 &9473 \\ Car10pa&32835 &28722 & -4813& n.a. & n.a. & 1583 & 12492 &30359 \\ Car10pb&14282 &12546 &-14944& n.a. & n.a. & -5782 & 9934 &13361 \\ Car10pc&14919 &12296 &-17140& n.a. & n.a. & -8040 & 2473 &13655 \\ \hline Esc08a & 2 & 0 & -2 & 0 & n.a. & -2 & 0 & 2 \\ Esc08b & 8 & 1 & -2 & 2 & n.a. & -2 & 3 & 6 \\ Esc08c & 32 & 13 & 8 & 22 & n.a. & 9 & 18 & 30 \\ Esc08d & 6 & 2 & -2 & 2 & n.a. & -2 & 2 & 6 \\ Esc08e & 2 & 0 & -6 & 0 & n.a. & -6 & -4 & 1 \\ Esc08f & 18 & 9 & 8 & 18 & n.a. & 9 & 13 & 18 \\ \hline Nug05 & 50 & 50 & 47 & 50 & 50 & 49 & 50 & 50 \\ Nug06 & 86 & 84 & 69 & 86 & 70 & 74 & 85 & 86 \\ Nug07 & 148 & 137 & 125 & 148 & 130 & 132 & 144 & 148 \\ Nug08 & 214 & 186 & 167 & 204 & 174 & 179 & 197 & 210\\ \hline \end{tabular} ~~\\ {Numerical Results for old instances} \end{center} \newpage \begin{center} \begin{tabular}{|l|rrrr|} \hline & Sol. & $\mu_{R1}$ &$\mu_{R2}$ & $\mu_{R3}$ \\ \hline Nug12C & 578 & 492 & 534 & 545 \\ Nug15C & 1150 & 1012 & 1075 & 1081 \\ Nug20C & 2570 & 2292 & 2396 & 2335 \\ Nug30C & 6124 & 5424 & 5648 & --~ \\ \hline \end{tabular} ~~\\ {Instances for which symmetry is destroyed} \end{center} %\begin{center} \begin{tabular}{|lc|rrr|rrrrrr|} \hline & $n$ & Sol. & GLB & ($ir$) & $\mu_{R1}$ & ($ir$) & $\mu_{R2}$ & ($ir$) &$\mu_{R3}$ & ($ir$)\\ \hline Nug12 & 12 & 578 & 493 & & 486 & & 530 & & 547 & \\ Nug12.1 & 11 & 586 & 496 & (0.6)& 514 & (5.4) & 551 & (3.9)& 574 & (4.9)\\ Nug12.2 & 11 & 578 & 495 & (0.4)& 514 & (5.4) & 553 & (4.3)& 571 & (4.3)\\ Nug12.5 & 11 & 578 & 494 & (0.2)& 524 & (7.8) & 552 & (4.1)& 570 & (4.2)\\ Nug12.6 & 11 & 586 & 499 & (1.2)& 530 & (9.0) & 561 & (5.8)& 578 & (5.6)\\ \hline Nug15 & 15 & 1150 & 963 & & 1009& & 1060& & 1075& \\ Nug15.1 & 14 & 1150 & 967 &(0.4)& 1049&(4.0)& 1104&(4.2)& 1114&(3.6)\\ Nug15.2 & 14 & 1166 & 974 &(1.1)& 1076&(6.6)& 1124&(6.0)& 1135&(5.6)\\ Nug15.3 & 14 & 1200 & 987 &(2.5)& 1075&(6.5)& 1133&(6.9)& 1145&(6.5)\\ Nug15.6 & 14 & 1152 & 968 &(0.5)& 1056&(4.7)& 1106&(4.3)& 1118&(4.0)\\ Nug15.7 & 14 & 1166 & 979 &(1.7)& 1052&(4.3)& 1112&(5.2)& 1125&(4.7)\\ Nug15.8 & 14 & 1168 & 983 &(2.1)& 1063&(5.4)& 1118&(5.5)& 1133&(5.4)\\ \hline Nug20 & 20 & 2570 & 2057& & 2281& & 2385& & 2326 & \\ Nug20.1 & 19 & 2628 & 2082&(1.2)& 2358&(3.4)& 2449&(2.7)& 2414 &(3.8) \\ Nug20.2 & 19 & 2600 & 2130&(3.6)& 2401&(5.3)& 2489&(4.4)& 2464 &(6.0) \\ Nug20.3 & 19 & 2588 & 2067&(0.5)& 2331&(2.2)& 2428&(1.8)& 2392 &(2.8) \\ Nug20.6 & 19 & 2570 & 2064&(0.3)& 2341&(2.6)& 2431&(1.9)& 2403 &(3.3) \\ Nug20.7 & 19 & 2634 & 2105&(2.3)& 2387&(4.6)& 2479&(3.9)& 2436 &(4.7) \\ Nug20.8 & 19 & 2636 & 2127&(3.4)& 2381&(4.4)& 2485&(4.2)& 2438 &(4.8) \\ \hline \end{tabular} %\end{center} ~~\\ Results for first level in branching tree \end{document}